We have studied non-adiabatic spin-dependent transport through ballistic conductors of different shape (straight and ring-type geometries) subject to inhomogeneous magnetic fields of varying strength. Our account generalizes studies of the regime of adiabatic spin-transport, widely discussed in the literature15,21,33,44. This regime is included here as the strong field limit.
For straight conductors we discussed several spin effects in the quantized conductance.
In particular we found a strong enhancement of the adiabatic spin channel each time a new transverse mode opens in the conductor, owing to the fact that electrons propagate slowly within the channel corresponding to the new mode.
For ring geometries we obtain numerically the explicit dependence of the transmission on the scaled field strength Q, which acts as an adiabaticity parameter, elucidating the rˆole of geometrical phases in ballistic quantum transport and possible experimental realizations.
Moreover, for in-plane field configurations and symmetric ballistic ring microstructures we demonstrate how an additional small flux φ can be used to control the spin dynamics and thereby tune the polarization of transmitted electrons25. This quantum mechanism, which is analytically investigated in detail in a subsequent paper1 does not require adiabaticity. We
0 1
(a)
0 1
〈Td(E,φ)〉E
(↓↑)d (↑↑)d
(↑↑+↓↑)d (b)
0 1
0 0.5 1
φ/φo (c)
FIG. 14: Diagonal contribution (in mode number) to the multichannel averaged tranmission of Fig. 13. The overall diagonal transmission hTdi (solid line) is split into its components hTd↑↑i = hT11↑↑i+hT22↑↑i(dashed) and hTd↓↑i=hT11↓↑i+hT22↓↑i (dotted). Note the similarity with the results of Fig. 7.
have also assessed in detail the range of validity of the spin-switch effect for various different situations relaxing constraints on symmetry, field configuration, and channel number. In combination with a spin detector such a device may be used to control spin polarized current, similar to the spin field-effect transistor proposed in Ref. 3. For metallic, generally diffusive conductors disorder breaks the spatial symmetry. We found numerically that the spin switch mechanism no longer prevails for diffusive rings51.
Finally, we point out that ballistic rings with Rashba (spin-orbit) interaction52, yielding an effective in-plane magnetic field in the presence of a vertical electric field, exhibit a similar spin-switch effect53.
0 0.8 (a)
0 0.8
〈Tnd(E,φ)〉E
(↓↑)nd (↑↑)nd
(↑↑+↓↑)nd (b)
0 0.8
0 0.5 1
φ/φo (c)
FIG. 15: Off-diagonal contribution (in mode number) to the multichannel averaged tranmission of Fig. 13. The overall off-diagonal transmission hTndi (solid line) is split into its components hTnd↑↑i =hT12↑↑i+hT21↑↑i (dashed) andhTnd↓↑i = hT12↓↑i+hT21↓↑i (dotted). Note the contrast with the complementary diagonal contribution in Fig. 14.
Acknowledgments
A larger part of this work was performed at the Max-Planck-Institut for the Physics of Complex Systemsin Dresden, Germany. We thank the institute and particularly P. Fulde for continuous support. We gratefully acknowledge financial support from the Alexander von Humboldt Foundationand theDeutsche Forschungsgemeinschaftthrough the research group Ferromagnet-Semiconductor Nanostructures. We also thank J. Fabian, H. Schomerus, and
D. Weiss for many useful discussions.
∗ Present address: NEST-INFM & Scuola Normale Superiore, 56126 Pisa, Italy.
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